LIRa session: Thomas Schindler

Speaker: Thomas Schindler (University of Amsterdam)

Date and Time: Thursday, November 24th 2022, 16:30-18:00

Venue: ILLC seminar room F1.15 in Science Park 107 and online.

Title: Unrestricted quantification, higher order logic, and type-free theories

Abstract. Call a quantifier ‘unrestricted’ if it ranges over absolutely all objects. Arguably, unrestricted quantification is often presupposed in philosophical inquiry. However, developing a semantic theory that vindicates unrestricted quantification proves rather difficult, at least as long as we formulate our semantic theory within a classical first-order language. It has been argued that using a type theory (higher order logic) as framework for our semantic theory provides a resolution of this problem, at least if a broadly Fregean interpretation of type theory is assumed (e.g. Williamson 2003). However, the intelligibility of this interpretation has been questioned. In this paper I introduce a type-free theory of properties that can also be used to vindicate unrestricted quantification. Although this alternative theory is formulated in a non-classical logic, it preserves the deductive strength of classical strict type theory in a natural way.